1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)
=[1/x-1/(x+3)+1/(x+3)-1/(x+6)+1(x+6)-1/(x+9)]/3
=[1/x-1/(x+9)]/3
=3/x(x+9)
=3/2x+18
2x+18=x(x+9)
x²+7x-18=0
(x-2)(x+9)=0
x1=2x2=-9(经检验知,不合舍去）
所以,x=2是原分式方程的解
1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)=3/2x+18
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